The Decision Model and Notation (DMN) is a standard notation to
capture decision logic in business applications in general and
business processes in particular. A central construct in DMN is
that of a decision table. The increasing use of DMN decision tables
to capture critical business knowledge raises the need to support
analysis tasks on these tables such as correctness and completeness
checking. This paper provides a formal semantics for DMN tables, a
formal definition of key analysis tasks and scalable algorithms to
tackle two such tasks, i.e., detection of overlapping rules and of
missing rules. The algorithms are based on a geometric
interpretation of decision tables that can be used to support other
analysis tasks by tapping into geometric algorithms. The algorithms
have been implemented in an open-source DMN editor and tested on
large decision tables derived from a credit lending dataset.